望采纳
如图
e^y +xy =e
x=0
e^(y(0)) + 0 =e
y(0) =1
e^y +xy =e
两边求导
y'.e^y +( y + xy' ) = 0
y'(0).e^(y(0)) +( y(0) +0) =0
y'(0). e + 1 =0
y'(0) = -1/e
y'.e^y +( y + xy' ) = 0
两边求导
[y''+(y')^2 ].e^y + ( y' + xy'' + y' ) = 0
[y''(0)+(y'(0))^2 ].e^(y(0)) + ( y'(0) + x(0).y''(0) + y'(0) ) = 0
[ y''(0) +1/e^2 ] . e + (-1/e + 0 -1/e ) = 0
e.y''(0) = 1/e
y''(0) = 1/e^2
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